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Q.

The velocities of three particles of masses 20g, 30g and 50g are 10i, 10 j and 10k respectively. The velocity of the centre of mass of the three particles is

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a

$10 (\vec{i} + \vec{j} + \vec{k})$

b

$20 \vec{i} + 30 \vec{j} + 5 \vec{k}$

c

$2 \vec{i} + 3 \vec{j} + 5 \vec{k}$

d

$20 \vec{i} + 30 \vec{j} + 50 \vec{k}$

answer is A.

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Detailed Solution

$\begin{aligned} v_{c m} = \frac{m_{1} {\vec{v}}_{1} + m_{2} \vec{v_{2}} + m_{3} \vec{v_{3}}}{m_{1} + m_{2} + m_{3}} \\ = \frac{20 \times 10 \hat{i} + 30 \times 10 \hat{j} + 50 \times 10 \hat{k}}{20 + 30 + 50} \\ = \frac{200 \hat{k} + 300 j + 500 k}{100} \\ = \frac{2 \hat{i} + 3 \hat{j} + 5 \hat{k}}{1} \end{aligned}$

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